Question

roger bowled 7 games last weekend. his scores are: 155, 165, 138, 172, 127, 193, 142. what is the range of rogers scores? a) 193 b) 68 c) 60 d) 127 at donalds donuts the number of donut holes in a bag can vary. help donald find the mode. 12, 10, 10, 10, 13, 12, 11, 13, 10 a) 13 b) 10 c) 12 d) 11 7. what is the sample standard deviation for the data given: (12, 13, 29, 18, 61, 35, 21) a) 41.98 b) 293.67 c) 17.14 d) 15.87 8. to find the ____ you add up all the numbers and then divide by how many numbers you have. a) mean b) range c) mode d) median

Explanation:

Step1: Find the range of Roger's scores

Range is the difference between the highest and lowest values. The scores are 155, 165, 138, 172, 127, 193, 142. The highest value is 193 and the lowest is 127. So, $193 - 127=66$.

Step2: Find the mode of the donut - hole data

The mode is the number that appears most frequently. The data set is 12, 10, 10, 10, 13, 12, 11, 13, 10. The number 10 appears 4 times, more frequently than any other number.

Step3: Calculate the sample standard deviation

1. First, find the mean $\bar{x}$ of the data set $\{12, 13, 29, 18, 61, 35, 21\}$. $\bar{x}=\frac{12 + 13+29+18+61+35+21}{7}=\frac{189}{7}=27$.
2. Then, find the squared - differences $(x_i-\bar{x})^2$ for each data point:

• $(12 - 27)^2=(-15)^2 = 225$
• $(13 - 27)^2=(-14)^2 = 196$
• $(29 - 27)^2=2^2 = 4$
• $(18 - 27)^2=(-9)^2 = 81$
• $(61 - 27)^2=34^2 = 1156$
• $(35 - 27)^2=8^2 = 64$
• $(21 - 27)^2=(-6)^2 = 36$

1. The sum of squared - differences $\sum_{i = 1}^{n}(x_i-\bar{x})^2=225+196 + 4+81+1156+64+36=1762$.
2. The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{1762}{6}\approx293.67$.
3. The sample standard deviation $s=\sqrt{s^2}=\sqrt{293.67}\approx17.14$.

Step4: Recall the definition of mean

The mean is calculated by adding up all the numbers and then dividing by the number of numbers.

Answer:

1. b) 66
2. b) 10
3. c) 17.14
4. a) Mean