Question

1. What is the mean of the sample values 2 cm, 2 cm, 3 cm, 5 cm, and 8 cm?

2. What is the median of the sample values listed in Exercise 1?

3. What is the mode of the sample values listed in Exercise 1?

4. If the standard deviation of a data set is 5.0 ft, what is the variance?

5. If a data set has a mean of 10.0 seconds and a standard deviation of 2.0 seconds, what is the z score corresponding to the time of 4.0 seconds?

6. Fill in the blank: The range, standard deviation, and variance are all measures of _____.

7. What is the symbol used to denote the standard deviation of a sample, and what is the symbol used to denote the standard deviation of a population?

8. What is the symbol used to denote the mean of a sample, and what is the symbol used to denote the mean of a population?

9. Fill in the blank: Approximately _____ percent of the values in a sample are greater than or equal to the 25th percentile.

10. True or false: For any data set, the median is always equal to the 50th percentile.

Answer 1

Solution:-
1 Given that values 2,2,3,5,8

Mean = sum of terms/number of terms = 20/5 = 4

2. Median = 3

Explanation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

2 2 3 5 8

So, the median is 3 .

3. Mode = 2

Explanation

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

2 2 3 5 8

We see that the mode is 2 .

4. Given that standard deviation = 5.0 ft,

variance = 5^2 = 25

5. z = (x - μ) / σ

z = (4.0-10.0)/2.0

z = -3.0

6. The range, standard deviation, and variance are all measures of variation

7. Standard deviation symbols:
σ used for the population standard deviation.
s used for the sample standard deviation.

8. Mean symbols

μ is the population mean

X-bar is the sample mean

9.
Approximately 75 percent of the values in a sample are greater than or equal to the 25th percentile.

10.
For any data set, the median is always equal to the 50th percentile. --> True