Question

essential learnings: mean, median, mode, range quiz correctives
multiple choice
identify the choice that best completes the statement or answers the question.

1. find the mean of the data set 18, 36, 24, 36, 30, and 36.

a. 26
b. 27
c. 36
d. 30

1. find the mean, median, mode, and range of the data set.

| number of books read |
| ---- |

sylvester 218	edmund 224
rashim 217	treyu 217

a. the mean is 217.5 books; the median is 219 books; the mode is 217 books; and the range is 7 books.
b. the mean is 219 books; the median is 217 books; the mode is 217.5 books; and the range is 7 books.
c. the mean is 219 books; the median is 217.5 books; the mode is 217 books; and the range is 7 books.
d. the mean is 219 books; the median is 217.5 books; the mode is 7 books; and the range is 217 books.

1. find a set of 5 items that has a range of 9, a mean of 15, a median of 14, and a mode of 11.

a. 11, 11, 13, 15, 20
b. 5, 11, 14, 14, 31
c. 11, 11, 14, 19, 20
d. 6, 10, 14, 15, 15
find the mean of the data.

1. 17, 27, 26, 2, 1, 21, 13, 16, 19, 5, 7

a. 10.5
b. 21
c. 14
d. 6
find the median of the data.

1. 53, 62, 30, 30, 64

a. 53
b. 52
c. 30
d. 48
find the mode(s) of the data.

1. 92, 97, 92, 96, 98, 94

a. 98, 92
b. 94
c. 92
d. no mode

Explanation:

Step1: Recall mean formula

The mean of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.

Step2: Calculate mean for question 1

For the data - set $18,36,24,36,30,36$, $n = 6$ and $\sum_{i=1}^{6}x_i=18 + 36+24 + 36+30+36=180$. Then $\bar{x}=\frac{180}{6}=30$.

Step3: Calculate mean, median, mode and range for question 2

The data - set is $217,217,218,224$.

• Mean: $\bar{x}=\frac{217 + 217+218+224}{4}=\frac{876}{4}=219$.
• Median: Arrange in ascending order $217,217,218,224$. Since $n = 4$ (even), median $=\frac{217 + 218}{2}=217.5$.
• Mode: The number that appears most frequently is $217$.
• Range: $224−217 = 7$.

Step4: Check values for question 3

• For option a: The data - set is $11,11,13,15,20$. Range is $20 - 11=9$, mean is $\frac{11 + 11+13+15+20}{5}=\frac{70}{5}=14

eq15$.

• For option b: The data - set is $5,11,14,14,31$. Range is $31 - 5 = 26

eq9$.

• For option c: The data - set is $11,11,14,19,20$. Range is $20 - 11=9$, mean is $\frac{11+11 + 14+19+20}{5}=\frac{75}{5}=15$, median is $14$, mode is $11$.
• For option d: The data - set is $6,10,14,15,15$. Range is $15 - 6 = 9$, mean is $\frac{6+10+14+15+15}{5}=\frac{60}{5}=12

eq15$.

Step5: Calculate mean for question 4

The data - set is $1,2,5,7,13,16,17,19,21,26,27$. $n = 11$ and $\sum_{i = 1}^{11}x_i=1+2+5+7+13+16+17+19+21+26+27 = 154$. Mean $\bar{x}=\frac{154}{11}=14$.

Step6: Calculate median for question 5

Arrange the data - set $30,30,53,62,64$ in ascending order. Since $n = 5$ (odd), the median is the middle - value, which is $53$.

Step7: Find mode for question 6

The data - set is $92,97,92,96,98,94$. The number $92$ appears twice and the other numbers appear once, so the mode is $92$.

Answer:

1. d. 30
2. c. The mean is 219 books; the median is 217.5 books; the mode is 217 books; and the range is 7 books.
3. c. 11, 11, 14, 19, 20
4. c. 14
5. a. 53
6. c. 92