Statistical Data - Quantitative and Qualitative

There are two general types of data. 

Quantitative data is information about quantities that is, information that can be measured and written down with numbers. Some examples of quantitative data are your height, your shoe size, and the length of your fingernails. Speaking of which, it might be time to call Guinness. You've got to be close to breaking the record.

Qualitative data is information about qualities information that can't actually be measured. Some examples of qualitative data are the softness of your skin, the grace with which you run, and the color of your eyes. However, try telling Photoshop you can't measure color with numbers.

Here's a quick look at the difference between qualitative and quantitative data.

The age of your car. (Quantitative.)

The number of hairs on your knuckle. (Quantitative.)

The softness of a cat. (Qualitative.)

The color of the sky. (Qualitative.)

The number of pennies in your pocket. (Quantitative.)


** Remember, if we're measuring a quantity, we're making a statement about quantitative data. If we're describing qualities, we're making a statement about qualitative data. Keep your L's and N's together and it shouldn't be too tough to keep straight.

Find Mean, Mode and Median for Grouped data

The Histogram shows an even spread of data, indicating that sometimes the Coffee Shop is very busy, while other times they are making less than eight cappuccinos per hour.We now want to find the Average Number of Cappuccinos made every hour.

There are three types of Averages:

The Mean
The Median
The Mode

In this topic we calculate all three of these averages for the coffee shop example.

Finding the Range

The “Range” is the easiest Statistic to determine for Grouped Data. We simply take the end of the Highest Interval, and subtract the Beginning of the first Interval.

Range = Maximium – Minimum

For our Coffee Statistics, the Highest Group is 16-19, so our High Value “Maximum” is 19. The Lowest Group is 0-3, so the Low Value “Minimum” is zero.

Range = Maximium – Minimum = 19 – 0 = 19
The Range can also be stated as “0 to 19″



The Modal Class

The “Mode” is what happens most of the time, or on most occassions.

The “Mode” is the simplest Grouped Average to find.
It can be read straight from the Frequency Table, or straight from the Graph.

Sometimes we have more than one Group which is the most popular.

In these situations, we can have a two modes or a “Bimodal” situation, or three modes which is called “Trimodal”.

The Median Class

Finding the Median Class involves some working out steps to be applied to our original Frequency Table. There are three Main Steps:

1) Finding the half-way midpoint in the Frequency values.

2) Adding a third column to our Frequency Table where we calculate “Cumulative Frequency” values.

3) Locating the half-way point in the Cumulative Frequency Column, and then seeing which Class Interval lines up with this half-way point.

How we do each of these steps is as follows.

There are two ways to find the half-way midpoint in the Frequency values.

We can either write out the numbers from 1 to the Total frequency value and manually find the middle; or we can use a simple math formula to find this value.

Rather than writing out a long list of numbers, It is much easier to use the formula: 

Middle = Total Frequency + 1 and then divide by 2.

Find Mean, Mode, Median with Frequency Table

Find the mean, median and mode for this grouped data of test scores.

Scores   Frequency
   65                2
   70                3
   75                2
   80                5
   85                8
   90                7
   95                5
   100              3

This problem could be solved by entering ALL 35 scores into one list, with the score 65 appearing twice, 70 appearing 3 times, and so on.  But if we deal with the data as we deal with a frequency histogram, we can accomplish our task more quickly.

Enter the scores into L 1 and the frequencies into L 2 .
(See Basic Commands for entering data.)

Find the Mean and Median:

Method 1: (fast and easy )
Press 2nd MODE (QUIT) to return to the home screen.
Press 2nd STAT (LIST). Arrow to the right to
MATH.
Choose option #3: mean( if you want the mean.

Choose option #4: median( if you want the median.

Your choice will appear on the home screen waiting for you to tell it which list to use. This time we will tell the calculator the list containing the scores AND the list containing the frequencies. Notice the comma separating the lists.

Remember the List names appear on the face of the calculator above the number keys 1-6.

Find the Mean and Median:

Method 2: (a bit more sophisticated)
Press STAT. Arrow to the right to CALC. Now choose option #1: 1-Var Stats .

When 1-Var Stats appears on the home screen, tell the calculator the name of the list containing the scores AND the name of the list containing the frequency
(such as: 1-Var Stats L1, L2)

Press ENTER.

Arrow up and down the screen to see the statistical information about the data.

Find the Mode: The mode can be quickly determined by examining the chart to see which score occurred most often. No calculator work needed.
The mode is 85.

Test: Mean, Mode and Median

Questions and Answers

1. Find the mean in the following numbers:19, 21, 18, 17, 18, 22, 46

A. 23
B. 16
C. 19
D. 500
None of the above

2. What is the median in the following numbers:19, 21, 18, 17, 18, 22, 46

A. 15
B. 19
C. 21
D. 22
None of the above

3. What does mean, mean?

4. What does median mean?

5. What does mode mean?

6. What does range mean?

7. Find the mean in the following numbers:9, 8, 15, 8, 20

A. 12
B. 16
C. 15
D. 10
None of the above

8. Find the median in the following numbers:9, 8, 15, 8, 20

A. 20
B. 15
C. 9
D. 22
None of the above

9. Find the mode in the following numbers:9, 8, 15, 8, 20

A. 15
B. 8
C. 9
D. 20
None of the above

10. Find the range in the following numbers:9, 8, 15, 8, 20

A. 12
B. 900
C. 14
D. 15
None of the above

11. Find the mean in the following numbers:36, 38, 33, 34, 32, 30, 34, 35

A. 54
B. 34
C. 74
D. 44
None of the above

12. Find the median in the following numbers:36, 38, 33, 34, 32, 30, 34, 35

A. 34
B. 55
C. 23
D. 45
None of the above

13. Find the mode in the following numbers:36, 38, 33, 34, 32, 30, 34, 35

A. 34
B. 38
C. 36
D. 30
None of the above

More examples for you :)

Okay guys, here i posted more examples about the
measures of central tendency :)

Example No.1

Find the mean, median and mode for the following data:

5, 15, 10, 15, 5, 10, 10, 20, 25, 15

(You will need to organize the data.)

5, 5, 10, 10, 10, 15, 15, 15, 20, 25

Mean: Sum of all data ÷ No.of terms


130 / 10  = 13 (ans)

Median: 5, 5, 10, 10, 10, 15, 15, 15, 20, 25

**  Listing the data in order is the easiest way to find the median.

The numbers 10 and 15 both fall in the middle.
Average these two numbers to get the median.
10 + 15 =12.5 / 2
               = 6.25 (ans)

Mode: Two numbers appear most often: 10 and 15.

There are three 10's and three 15's.

In this example there are two answers for the mode.


Example No.2

For what value of x will 8 and x have the same mean (average) as 27 and 5?

First, find the mean of 27 and 5:
27 + 5 = 16 / 2

Now, find the x value, knowing that the average of x and 8 must be 16:

x + 8 ÷ 2 = 16

32 = x + 8 cross multiply

-8 - 8

= 24 (ans)


Example No.3

On his first 5 biology tests, Bob received the following scores: 72, 86, 92, 63, and 77. What test score must Bob earn on his sixth test so that his average (mean score) for all six tests will be 80? Show how you arrived at your answer.

Possible solution:

Set up an equation to represent the situation. Remember to use all 6 test scores:
72 + 86 + 92 + 63 + 77 + x = 80 / 6

cross multiply and solve: (80)(6) = 390 + x

480 = 390 + x

- 390   -390

90 = x

Bob must get a 90 on the sixth test.


Example No.4

The mean (average) weight of three dogs is 38 pounds. One of the dogs, Sparky, weighs 46 pounds. The other two dogs, Eddie and Sandy, have the same weight. Find Eddie's weight.

Let x = Eddie's weight ( they weigh the same, so they are both represented by " x ".)
Let x = Sandy's weight

Average:   sum of the data divided by the number of data.

x + x + 46 = 38 cross multiply and solve
3(dogs)
(38)(3) = 2x + 46
114 = 2 x + 46

-46 -46
68 = 2x
2 2
34 = x Eddie weighs 34 pounds.

Do it yourself !

Here I posted a simple question on finding the Mean, Mode, Median and Range. Yet, it might be easy but once you do it careless, you might get the answer wrong :)

Stated below is the age of 8 siblings.

Hanna 67

Marissa 50

Mark 50

Brian 44

Mick 36

Kim 34

Rose 32

Nora 30

• Noted, Marissa and Mark are twins :)

Find,

(a) Mean

(b) Mode

(c) Median

(d) Range

WARM UP question !

Come on guys, try this out ! 

The list gives the scores a group of students who took part in a mathematics quiz.

10, 7, 14, 38, 26, 16, 10, 21

Find:


(a) Mode

= 10 (the most popular number)

(b) Mean

:  10 + 7 + 14 + 38 + 26 + 16 + 10 + 21 / 8 = 17.75 (Plus all the numbers and then divided by how many terms)

(c) Median

: Arranged the numbers from the smallest to biggest

7 , 10 , 10, 14 , 16, 21, 26, 38

Since there is 14 and 16 are the middle numbers. Plus 14 + 16 then divided it into 2. The answer is 15.

(d) Range

: This will be the simplest one. Just subtract the highest number with the smallest one.

38 - 7 = 31 (ans)

(e) The lower and upper quartile

: there is three quartile altogether

• lower quartile
• middle quartile
• upper quartile

So to find the:

Lower quartile -> 1/4 × 8 (no.of terms)
= 2.

Upper quartile -> 3/4 × 8 (no.of.terms)
= 6.

Lower = 10.
Upper = 26.

(d) The inter quartile range

: Minus the upper quartile - lower qurtile

26 - 10 = 16 (ans)