Question
Asked Feb 25, 2019
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You recorded the time in seconds it took for 8 participants to solve a puzzle. The times were: 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4. a. Find the mean b. Find the median c. Write the 5-number summary for this data

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Expert Answer

Step 1

a.

Obtain mean time took by participants to solve the puzzle.

The data represents the time in seconds took by a sample of 8 participants to solve a puzzle.

Mean:

Mean is a measure of center in case of quantitative data. Mean of a data set is the sum of the data set divided by the size.

The general formula for mean is,

x-bar=sum of observations xi/total number of observations.

Consider the variable X represents the time in seconds took by a sample of 8 participants to solve a puzzle.

The data points of the variable are X: 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1 and 29.4.

The mean time took by participants to solve the puzzle is obtained as 20.8125 seconds from the calculation given below:

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Step 2

b.

Obtain the median time took by participants to solve the puzzle.

The median of the dataset is nothing but the second quartile of dataset.

The data points of the variable X is arranged in ascending order as follows:

15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1 and 29.4.

The number of observations in the dataset is n = 8.

Since, 8 is an even number, the median of the data will be the average of middle two observations of the ordered dataset.

The median time took by participants to solve the puzzle is obtained as 19.95 seconds from the calculation given below:

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Step 3

c.

Five number summary of a dataset:

The five number summary of any dataset contains the values of minimum, first quartile, median, third quartile and maximum of the dataset.

Obtain the first quartile of the dataset.

The first quartile of the data is the median of the lower half of the ordered dataset.

Here, the values of lower half of the ordered dataset are 15.5, 18.8, 19.3 and 19.7.

The number of observations i...

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