Question

Trudy has been training for an upcoming marathon. She has kept track of how many miles she runs every day for the past two weeks:

12, 15, 7, 14, 12, 3, 16, 15, 19, 20, 12, 9, 18, and 21.

a. Calculate the mean and median for this data.

Mean:
Median

b. Calculate the Quartile 1 (Q1)
Quartile 2 (Q2)

d. What is the IQR (Interquartile Range):

Answer 1

Kindly check explanation

Explanation:

Given the data:

12, 15, 7, 14, 12, 3, 16, 15, 19, 20, 12, 9, 18, 21

Reordering the data:

3, 7, 9, 12, 12, 12, 14, 15, 15, 16, 18, 19, 20, 21

Mean = Σx / n = 193 / 14 = 13.76

The Median :

1/2(n+1)th term

15/2 = 7.5th term

(14 + 15) / 2 = 14.5

First quartile (Q1) :

1/4(n+1)th term

15/4 = 3.75th term

= 12

Q3 :

3/4(15)th term = 11.25 th term

Q3 = 18

Interquartile range = Q3 - Q1

Interquartile range = 18 - 12 = 6