18.09 Interquartile range

For each of the following sets of scores:

Consider the following data set containing 30 scores:

10, 13, 15, 24, 32, 42, 46, 53, 58, 64

11, 14, 16, 27, 33, 42, 49, 53, 60, 67

11, 15, 18, 28, 37, 44, 51, 55, 61, 67

Find the interquartile range for the following data set containing 20 scores:

5, 8, 11, 12, 12, 14, 15, 15, 18, 18, 19, 21, 21, 25, 29, 32, 33, 37, 38, 38

For each of the following data sets:

If there are 78 scores in a set of data, in which position will the lower quartile lie?

The following list shows the number of points scored by a basketball team in each game of their previous season:

The following data set shows Ray's scores from her last 13 rounds of golf played:

66, 66, 68, 68, 70, 78, 80, 84, 106, 116, 126, 130, 132

The following data set shows Luke's scores from his last 17 exams:

42, 46, 48, 51, 52, 54, 56, 68, 72, 76, 78, 82, 85, 86, 88, 92, 96

There is a test to measure the Emotional Quotient (EQ) of an individual. Here are the EQ results for 21 people listed in ascending order:

90,\, 90,\, 91,\, 92,\, 93,\, 94,\, 95,\, 95,\, 95,\, 97,\, 99,\, 100,\, 108,\, 114,\, 116,\, 116,\, 117,\, 118,\, 118,\, 122,\, 129

In a competition, a contestant must complete 12 challenges earning as many points as possible. Her scores for the first 11 challenges are:

38, 43, 45, 66, 67, 82, 92, 102, 105, 108, 119

Determine her score in the 12th round if the lower quartile of all of her 12 scores is 55.

The stem-and-leaf plot shows the number of hours students spent studying during an entire semester:

Below is the luggage weight of 30 passengers:

A group of students were asked how many phone calls they had made the previous day. The information was collected in the following frequency table:

The bar graph shows the marks (out of 10) that students received on a spelling test:

a

Find the lower quartile of the set of scores.

b

Find the upper quartile of the set of scores.

c

Find the interquartile range.

d

Explain the effect the scores less than 7 have on the summary statistics.

The stem-and-leaf plot shows the batting scores of two cricket teams, A and B:

To gain a place in the main race of a car rally, teams must compete in a qualifying round. The median time in the qualifying round determines the cut off time to make it through to the main race. Below are some results from the qualifying round:

• 75\% of teams finished in 159 minutes or less.

• 25\% of teams finished in 132 minutes or less.

• 25\% of teams finished between with a time between 132 and 142 minutes.