Sec 2 Mathematics Data Analysis: Averages topical questions

A data set reads 6, 3, 8, 4, 9, 6.

1. (a)Find the mean.[2]
2. (b)Find the median.[1]
3. (c)Find the mode.[1]

Four values have a mean of 7. Three of them are 5, 9 and 6.

1. (a)Find the total of the four values.[1]
2. (b)Find the fourth value.[1]
3. (c)A fifth value of 10 is added. Find the new mean.[2]

A dot diagram shows: value 1 with 2 dots, value 2 with 5 dots, value 3 with 3 dots, value 4 with 1 dot.

1. (a)State the mode.[1]
2. (b)State the median.[1]
3. (c)Find the mean, correct to 2 decimal places.[2]

A data set reads 5, 5, 8, 10, 12.

1. (a)Find the mean.[1]
2. (b)Find the median.[1]
3. (c)Find the mode.[1]

The mean of 6 values is 11. Five of them are 8, 9, 12, 13 and 10.

1. (a)Find the total of all six values.[1]
2. (b)Find the sixth value.[1]

A stem-and-leaf diagram has: stem 1 with leaves 2, 5, 8; stem 2 with leaves 0, 3, 3, 7; stem 3 with leaves 1, 5.

1. (a)List all the values.[1]
2. (b)Find the median.[2]
3. (c)State the mode.[1]

The mean of 6 numbers is 14.5. Five of them are 12, 15, 9, 20 and 16.

1. (a)Find the sixth number.[2]
2. (b)The sixth number is removed. Find the mean of the remaining five.[2]

The mean mass of 8 boys is 52 kg.

1. (a)Find their total mass.[1]
2. (b)A ninth boy joins and the new mean is 53 kg. Find his mass.[2]
3. (c)Explain why the mean rose.[1]

Seven employees earn (in $ thousands): 18, 20, 20, 22, 24, 26 and 95.

1. (a)Find the mean salary, correct to 1 decimal place.[2]
2. (b)Find the median salary.[1]
3. (c)Which average describes a typical worker better? Give a reason.[1]

A stem-and-leaf diagram has: stem 1 with leaves 3, 6, 9; stem 2 with leaves 2, 2, 7; stem 3 with leaf 4.

1. (a)List all the values.[1]
2. (b)Find the median.[2]
3. (c)State the mode.[1]

The mean of 9 test scores is 62.

1. (a)Find the total of the 9 scores.[1]
2. (b)A 10th student scores 80. Find the new mean.[2]
3. (c)What score would have kept the mean at exactly 62?[1]

The marks of 40 pupils are grouped: 0–20: 4, 20–40: 10, 40–60: 16, 60–80: 8, 80–100: 2.

1. (a)State the modal class.[1]
2. (b)How many pupils scored at least 40?[1]
3. (c)Explain why the exact mean cannot be found from the table.[1]
4. (d)Estimate the mean using class midpoints.[2]

Class X’s marks are 62, 65, 68, 70, 70, 72, 75, 75, 78, 85. Class Y’s mean is 70 with a median of 71, and its marks run from 40 to 95.

1. (a)Find the mean of Class X.[2]
2. (b)Find the median of Class X.[1]
3. (c)Compare the two classes’ averages and spreads, and state which class was more consistent.[2]

A quiz team’s mean score over 5 games is 18 points.

1. (a)Find their total points so far.[1]
2. (b)They score 27 in a 6th game. Find the new mean.[2]
3. (c)What score in the 6th game would have kept the mean at exactly 18?[2]

Two hawkers compare six days of takings in dollars. Ah Kow: 205, 210, 210, 210, 212, 213. Bee Leng: 180, 240, 190, 235, 200, 215.

1. (a)Find the mean takings of each hawker.[2]
2. (b)Find the median takings of each hawker.[2]
3. (c)Which hawker’s daily takings were more consistent? Justify briefly.[1]