3.015 Analysing data

What is the difference between the median and the mode?

State whether the following statements are true or false:

Find the mode of the following scores:

2, 2, 6, 7, 7, 7, 7, 11, 11, 11, 13, 13, 16, 16

State whether the following sets of numbers have a mean of 3:

Find the mean of the following sets of scores:

Find the median of the following set of scores: 6,\, 8,\, 9,\, 11,\, 16,\, 17,\, 18

For each of the following sets of scores:

State the position of the median in an ordered set of:

Find the sum of the following sets of scores:

Calculate the number of scores in the following sets:

The five numbers 16, 16, 17, 24, 17 have a mean of 18. If a new number is added that is bigger than 24, will the mean be higher or lower?

The five numbers 11, 13, 9, 13, 9 have a mean of 11. If a new number is added that is smaller than 9, will the mean be higher or lower?

Five numbers have a mean of 7. If four of the numbers are 10, 10, 8 and 7 and the last number is x, find the value of x.

The mean of four scores is 21. If three of the scores are 17, 3 and 8, find the fourth score.

The mean of a set of 41 scores is 18.6. If a score of 71.8 is added to the set, find the new mean. Round your answer to two decimal places.

Six numbers 6, 2, 7, 18, 17 and an unknown number x have a median of 8.5. Find the missing value x.

Find four consecutive odd numbers whose median is 40.

Five numbers have a range of 16, a mode of 2, a median of 7 and a mean of 8. The minimum number in the set is 2.

Three numbers have a mode of 10 and a mean of 10. Write the three numbers of the data set.

Four numbers have a range of 5, a median of 9 and a mode of 11. Write the four numbers of this data set.

Each of the following data sets are missing one score. Find the missing score if:

Find the range of the following sets of scores:

For each of the given sets of data find the following correct to two decimal places:

The range of a set of scores is 8, and the highest score is 19. What is the lowest score in the set?

The range of a set of scores is 22, and the lowest score is 13. What is the highest score in the set?

The five numbers 11, 13, 9, 13, 9 have a mean of 11 and sample standard deviation of 2. If a new number is added that is smaller than 9, will the standard deviation increase or decrease?

A data set has a mean of 10 and a standard deviation of 5. If a new score of 11.5 is added to the set, will the standard deviation increase or decrease?

Consider the following data set:

If one score of 8 is changed to a 9, which measure(s) of centre or spread would be altered?

Durations of calls (in minutes) made in a household were recorded as follows:

5,\text{ }\text{ } 11,\text{ }\text{ } 3,\text{ }\text{ } 9,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 14,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 5,\text{ }\text{ } 3,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 14,\text{ }\text{ } 5

A real estate agent wanted to determine a typical house price in a certain area. He gathered the selling price of some houses:

\$317\,000, \quad\$320\,000,\quad \$347\,000,\quad \$360\,000,\quad \$378\,000,\\\\ \$395\,000,\quad \$438\,000,\quad \$461\,000,\quad \$479\,000,\quad \$499\,000

The selling price of recently sold houses are shown below:

\$467\,000, \,\$413\,000,\, \$410\,000,\, \$456\,000,\, \$487\,000,\, \$929\,000

The table shows the number of goals scored by a football team in each game of the year:

A teacher calculated the mean of 25 students’ marks to be 64. A student who later completed the assessment got a mark of 55. Find the new mean of the class, to two decimal places.

Han wants to try out as a batsman for a cricket team. In his last three matches, he scored 61, 75 and 66 runs. In his last match before trying out, he wants to lift his mean to 70. If x is the number of runs he needs to score to achieve this, find x.

A group of students had a range in marks of 14 and the lowest score was 9. What was the highest score in the group?

Marge grows two different types of bean plants. She records the number of beans that she picks from each plant for 10 days. Her records are shown below:

• Plant A: \,10,\, 4,\, 4,\, 5,\, 7,\, 10,\, 3,\, 3,\, 9,\, 10

• Plant B: \,8,\, 7,\, 5,\, 5,\, 9,\, 7,\, 8,\, 7,\, 5,\, 6

The median house price in the suburb of Humbleton is \$950\,000 with a mean price of \$1\,000\,000 and the median house price in the suburb of Brockway is \$950\,000 with a mean price of \$880\,000.

Which suburb is more likely to have very expensive houses? Explain your answer.

The beaks of two groups of bird are measured, in millimetres, to determine whether they might be of the same species. The measurements are shown below:

• Group 1: \,33,\, 39,\, 31,\, 27,\, 22,\, 37,\, 30,\, 24,\, 24,\, 28

• Group 2: 29,\, 44,\, 45,\, 34,\, 31,\, 44,\, 44,\, 33,\, 37,\, 34

Two English classes, each with 15 students, sit a 10 question multiple choice test. Their class results, out of 10, are below:

• Class 1: \,3,\, 2,\, 3,\, 3,\, 4,\, 5,\, 1,\, 1,\, 1,\, 4,\, 2,\, 2,\, 3,\, 3,\, 2

• Class 2: \,8, \,9, \,9, \,8, \,8, \,6,\, 8,\, 10,\, 6,\, 8,\, 8,\, 9,\, 6,\, 9,\, 9

The hours of sleep per night for two people over a two week period are shown below:

• Person A: 8, \,5, \,10, \,7, \,9, \,7, \,6, \,10, \,6, \,9, \,7, \,7, \,10, \,5

• Person B: 8, \,8, \,8, \,7, \,7.5, \,8, \,7.5, \,7, \,7, \,7, \,7.5, \,7, \,7, \,7.5

The salaries of men and women working the same job at the same company are given below:

• Men: \$80\,000,\, \$80\,000,\, \$75\,000,\, \$80\,000,\, \$75\,000,\, \$70\,000,\, \$80\,000

• Women: \$70\,000,\, \$70\,000,\, \$75\,000,\, \$70\,000,\, \$70\,000,\, \$80\,000,\, \$75\,000

The following table shows the marks obtained by a student in two subjects: