13.03 Summarising data
Calculate the mean of the following data sets:
6, \, 4
8, \, 5
4, \, 8, \, 9, \, 12
7, \, 18, \, 9, \, 3
4, \, 10, \, 2, \, 9, \, 5
6, \, 14, \, 10, \, 13, \, 5, \, 9, \, 14, \, 15
11, \, 5, \, 14, \, 18, \, 15
8, \, 14, \, 24, \, 7, \, 12
13, \, 27, \, 9, \, 6, \, 8
13, \, 15, \, 7, \, 17, \, 9
State the mean of the following sets of data:
9, 9, 9, 9
2, 3, 4
850, 900, 950
Martha's grades in her 5 subjects are: 91, 93, 94, 90 and 92. Find the mean of Martha's grades.
Victoria has scored 12 goals this season, with a mean of 2 goals per game. How many games did she play?
James has played 10 games this season, with a mean of 1.5 goals per game. How many goals did he score in total?
Find the median of the following data sets:
2, \, 3, \, 4, \, 5, \, 6
6, \, 9, \, 3, \, 5, \, 4
1, \, 4, \, 6, \, 8
5, \, 5, \, 5, \, 5
22, \, 12, \, 19, \, 16
2, \, 4, \, 9, \, 10
3, \, 18, \, 10, \, 19, \, 12, \, 5, \, 6, \, 20, \, 7
7, \, 19, \, 6, \, 14, \, 18, \, 11
5.3, \, 8.4, \, 2.6, \, 4.7, \, 3.5
49.4, \, 25.4, \, 47.2, \, 34.2, \, 28.4, \, 32.2
A set of 15 scores is arranged in increasing order. In what position does the median score lie?
A set of 23 scores is arranged in increasing order. In what position does the median score lie?
A set of 12 scores is arranged in increasing order. Between which two scores does the median score lie?
A set of 34 scores is arranged in increasing order. Between which two scores does the median score lie?
Counting numbers in increasing order such as 4, 5, 6, 7 are called consecutive numbers. Write down five consecutive numbers whose median is 6.
Write down four consecutive odd numbers whose median is 12.
Write down four consecutive even numbers whose median is 15.
Find the median from the following frequency distribution tables:
| Score | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|
| Frequency | 1 | 2 | 3 | 4 | 5 |
| Score | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|
| Frequency | 1 | 4 | 1 | 4 | 4 |
| Score | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|
| Frequency | 2 | 7 | 3 | 1 | 5 |
| Score | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|
| Frequency | 1 | 2 | 5 | 5 | 2 |
| Score | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|
| Frequency | 1 | 2 | 5 | 5 | 1 |
| Score | 13 | 14 | 15 | 16 | 17 |
|---|---|---|---|---|---|
| Frequency | 5 | 4 | 1 | 3 | 5 |
Calculate the range of the following scores:
10, 16, 6, 18, 17, 11, 9, 15, 14Write down four whole numbers whose median is 14 and whose range is 3.
Write down four whole numbers whose median is 17 and whose range is 3.
For each of the following data sets, calculate:
The median
The mode
The range
| Score | 11 | 14 | 19 | 22 | 29 |
|---|---|---|---|---|---|
| Frequency | 10 | 13 | 4 | 7 | 12 |
| Score | 14 | 19 | 22 | 25 | 32 |
|---|---|---|---|---|---|
| Frequency | 9 | 14 | 12 | 1 | 10 |
A phone support centre tracks the length of calls made each day in minutes. During a shift one employee made calls of the following lengths:
2, \, 3, \, 3, \, 2, \, 2, \, 4, \, 4, \, 2, \, 5, \, 13
How many calls did the employee make during their shift?
Calculate the following for the length of calls made:
Mean
Median
Mode
Range
A student scored the following grades on his end of year tests:
87, \, 90, \, 85, \, 84, \, 89, \, 80, \, 85, \, 87, \, 87How many tests did the student take?
Calculate the following:
Mean
Median
Mode
Range
A statistician organised a set of data into a frequency table:
| Score | 31 | 32 | 33 | 34 | 35 |
|---|---|---|---|---|---|
| Frequency | 12 | 14 | 7 | 20 | 15 |
Find the total number of respondents the statistician surveyed.
Determine the following, rounding your answers to two decimal places:
Mean
Median
Mode
Range
The selling price of six houses are:
\$467\,000,\, \$413\,000,\, \$410\,000,\, \$456\,000, \,\$487\,000, \,\$929\,000Calculate the mean selling price, rounded to the nearest thousand dollars.
Which of the selling prices appears to be an outlier?
Recalculate the mean selling price, without the outlier.
The television show "Dragon Duels" ran for three seasons, each with 6 episodes. The average fan ratings (out of 10) for each episode are shown in the following table:
| Episode 1 | Episode 2 | Episode 3 | Episode 4 | Episode 5 | Episode 6 | |
|---|---|---|---|---|---|---|
| Season 1 | 8.2 | 8.4 | 7.9 | 7.9 | 8 | 8.2 |
| Season 2 | 8.2 | 8.6 | 9.1 | 7.8 | 8.8 | 8.4 |
| Season 3 | 8.9 | 9.4 | 9.2 | 9.7 | 7.4 | 4.3 |
Which episode appears to be an outlier?
Which season has the highest mean rating?
Which season has the highest median rating?
Which season has the highest range of ratings?