Questions: The prices of the 19 top-rated all-season tires for a specific tire size, are as follows. Answer parts (a) - (c). 88, 116, 98, 78, 82, 92, 94, 89, 94, 81, 108, 113, 100, 96, 86, 92, 74, 99, 91

The prices of the 19 top-rated all-season tires for a specific tire size, are as follows. Answer parts (a) - (c).
88, 116, 98, 78, 82, 92, 94, 89, 94, 81, 108, 113, 100, 96, 86, 92, 74, 99, 91

Transcript text: The prices of the 19 top-rated all-season tires for a specific tire size, are as follows. Answer parts (a) - (c). $88, $116, $98, $78, $82, $92, $94, $89, $94, $81, $108, $113, $100, $96, $86, $92, $74, $99, $91

Solution

Solution Steps

To solve the given problem, we need to perform the following steps:

(a) Calculate the mean price of the tires. (b) Calculate the median price of the tires. (c) Calculate the standard deviation of the tire prices.

Step 1: Calculate the Mean Price

The mean price of the tires is calculated by summing all the prices and dividing by the number of prices. Given the prices:

\[ \{88, 116, 98, 78, 82, 92, 94, 89, 94, 81, 108, 113, 100, 96, 86, 92, 74, 99, 91\} \]

The mean price is:

\[ \text{Mean} = \frac{\sum \text{prices}}{19} = 93.21 \]

Step 2: Calculate the Median Price

The median price is the middle value when the prices are arranged in ascending order. For 19 prices, the median is the 10th value in the sorted list. The sorted prices are:

\[ \{74, 78, 81, 82, 86, 88, 89, 91, 92, 92, 94, 94, 96, 98, 99, 100, 108, 113, 116\} \]

The median price is:

\[ \text{Median} = 92.0 \]

Step 3: Calculate the Standard Deviation

The standard deviation measures the amount of variation or dispersion of the prices. It is calculated using the formula:

\[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \]

Where $ \mu $ is the mean price and $ N $ is the number of prices. The standard deviation is:

\[ \sigma = 10.81 \]