Question

A grocery store owner polled ten customers to determine how many times they went to the grocery store in April. The results of his poll are shown below.

12,9,4,8,25,6,8,5,18,13
Determine the appropriate shape of the distribution.

A. The data does not show a latter

B. Left skewed

C. Symmetrical

D. Right skewed

Answer 1

D. Right skewed

Explanation:

To determine the shape of the distribution, we can examine the given data:

12, 9, 4, 8, 25, 6, 8, 5, 18, 13

One way to determine the shape of the distribution is by visualizing it using a histogram or a box plot. However, without the exact frequency of each value, we cannot create an accurate visual representation.

Alternatively, we can examine the skewness of the distribution. Skewness is a measure of the asymmetry of a distribution. If the data is skewed to the left, it is left-skewed or negatively skewed. If it is skewed to the right, it is right-skewed or positively skewed. If the data is symmetric and evenly distributed, it is considered a symmetrical distribution.

Let's calculate the skewness of the given data to determine the shape:

Skewness = (3 * (mean - median)) / standard deviation

First, let's calculate the mean, median, and standard deviation of the data:

Mean = (12 + 9 + 4 + 8 + 25 + 6 + 8 + 5 + 18 + 13) / 10 = 10.8

Median = the middle value when the data is arranged in ascending order:

4, 5, 6, 8, 8, 9, 12, 13, 18, 25

Median = (8 + 9) / 2 = 8.5

Next, let's calculate the standard deviation:

Step 1: Calculate the squared differences from the mean for each value:

(12 - 10.8)^2, (9 - 10.8)^2, (4 - 10.8)^2, (8 - 10.8)^2, (25 - 10.8)^2, (6 - 10.8)^2, (8 - 10.8)^2, (5 - 10.8)^2, (18 - 10.8)^2, (13 - 10.8)^2

Step 2: Calculate the sum of squared differences:

(1.44 + 2.88 + 45.76 + 8.64 + 228.01 + 22.09 + 8.64 + 32.49 + 47.04 + 4.84) = 411.73

Step 3: Calculate the variance:

Variance = sum of squared differences / (n - 1) = 411.73 / (10 - 1) = 45.75

Step 4: Calculate the standard deviation:

Standard deviation = square root of variance = √45.75 = 6.76 (approximately)

Now we can calculate the skewness:

Skewness = (3 * (mean - median)) / standard deviation

Skewness = (3 * (10.8 - 8.5)) / 6.76

Skewness = 6.4 / 6.76

Skewness ≈ 0.95

Since the skewness is positive (0.95), the data is right-skewed or positively skewed. Therefore, the appropriate shape of the distribution is:

D. Right skewed