Question

Consider the following data set: {4, 7, 11, 12, 18, 19, 20, 22, 23, 25}

Answer the following questions. If necessary, round your answers to four decimal places.

(a) Find the sample median of the data set.

(b) How much can you increase the smallest value from the data set without getting the value of the sample median changed? (Enter NA if there is no limit to the amount.)

(c) How much can you decrease the largest value from the data set without getting the value of the sample median changed? (Enter NA if there is no limit to the amount.)

Answer 1

4, 7, 11, 12, 18, 19, 20, 22, 23, 25

Number of observations = n = 10

median = mean of nth and nth + 1 observation

median = mean of 5th and 5th + 1 observation

median = mean of 5th and 6th observation

median = ( 18 + 19 )/2

median = 18.5

(b) How much can you increase the smallest value from the data set without getting the value of the sample median changed? (Enter NA if there is no limit to the amount.)

We can increase the value till 18 as it is involved in the median calculation

Increase = 18 - 4 = 14

How much can you increase the smallest value from the data set without getting the value of the sample median changed?

14

(c) How much can you decrease the largest value from the data set without getting the value of the sample median changed? (Enter NA if there is no limit to the amount.)

We can decrease the value till 19 as it is involved in the median calculation

Decrease = 25 - 19 = 6

How much can you decrease the largest value from the data set without getting the value of the sample median changed?

6