Question

Scores on the final in a statistics class are as follows.

75 25 75 52 80 85 80 99 90 60
86 92 40 74 72 55 87 70 85 70

Required:
a. Calculate the 25th, 50th, and 75th percentiles.
b. Calculate the interquartile range.
c. Construct a boxplot. Are there any outliers?

Answer 1

Kindly check explanation

Explanation:

Calculate the 25th, 50th, and 75th percentiles.

b. Calculate the interquartile range.

c. Construct a boxplot. Are there any outliers?

Reordered data:

25, 40, 52, 55, 60, 70, 70, 72, 74, 75, 75, 80, 80, 85, 85, 86, 87, 90, 92, 99

25 th percentile :

1/4 (n + 1)th, tetm

n = 20

1/4(21) = 5.25th term

(5 + 6) th term / 2

= 65

50th percentile :

1/2 (n + 1)th, tetm

n = 20

1/2(21) = 10.5th term

(10 + 11) th term / 2

= 75

75th percentile:

3/4 (n + 1)th, tetm

n = 20

3/4(21) = 15.75th term

(15 + 16) th term / 2

= 85.5

Interquartile range :

Q3 - Q1

75th percentile - 25th percentile

85.5 - 65

= 20.5

25 is an Outlier