Question

MT scores: 11, 11, 16, 17, 19, 20, 21, 21 23 24 24 26 26 27 27 28 28 28 29 30 31 31 32 33 35 37 38 38 39 42 44

Questions for Class MT Score Distribution Analysis

1. Create a boxplot of MT scores.

2. Compute the probability that a randomly selected student from the class scored higher than 20.

3. Are the MT scores normally distributed? Why or why not?

4. Assuming a normal fit, compute the percentile of your score.

5. Compute your actual percentile from the raw data.

6. Do your computations for #4 and 5 support your answer to #3? Why or why not?

Answer 1

1. Create a boxplot of MT scores.

First we arrange the data in ascending order.

X
11
11
16
17
19
20
21
23
24
24
26
26
27
27
28
28
28
29
30
31
31
32
33
35
37
38
38
39
42
44

For creating a box plot we need the min, Q1(lower quartile), median , 3rd quartile and the max.

The quartile formula

For eg: Q1 = 7.75th value where i = 1 and N = 30

= 7th + 0.75 (8th - 7th)

= 20 + 0.75 (21- 20)

= 20.75

Min	11
Q1	20.75
Median = Q2	27.5
Q3	32.25
Max	44

2. Compute the probability that a randomly selected student from the class scored higher than 20.

Here there are total of 30 students and no. of students who got above 20 = 24

P(higher than 20) = 24 / 30

3. Are the MT scores normally distributed? Why or why not?

If we look at the box plot in (1), we can see that the median line is slightly towards the right and there is more space on the left, which indicates that the distribution is skewed towards left. This is means it is not normally distributed since it is not symmetrical.

4. Assuming a normal fit, compute the percentile of your score.

If we want to use normal distribution we need the mean and SD. Here we have a sample so we will use sample SD.

Mean = = 835 / 30 = 27.833

SD =

= 8.449

z-score =

Assuming your score is 32

Percentile is like cumulative probability at a point.

P(X < 32) = P(Z < 0.49)

= 0.689 ..........................using normal probabiltiy tables

approx = 0.69

Percentile = probability * 100

5. Compute your actual percentile from the raw data.

We have the value of Pth value = 32

It ranks 23rd according to our data So = 23

The percentile of score 32 is 74th.

6. Do your computations for #4 and 5 support your answer to #3? Why or why not?

As we can see that the percentile score for 4 and 5 do not match (although don't highly differ as well since the skewness is very slightly seen). This is because the data is not normally distributed that answer will not match due to the skewness to the left shown by the data.