Question

The following data represent the amount of time​ (in minutes) a random sample of eight students took to complete the online portion of an exam in a particular statistics course. Compute the​ mean, median, and mode time.

65.4​, 79.5​, 83.2​, 113.5​, 128.4​, 99.3​, 94.7​, 115.2

Answer 1

The mean time is 97.4 minutes, the median is 97 minutes, and there is no mode as no values are repeated in the dataset. These measures are fundamental in understanding the central tendency of data in Statistics.

Step-by-step explanation:

The question involves calculating the mean, median, and mode for a given set of data, which are basic concepts of descriptive statistics in Mathematics. To find the mean, add all the time values and divide by the number of data points. For the median, list the data points in ascending order and find the middle value(s). If there's an odd number of data points, the median is the middle value. If there's an even number, the median is the average of the two middle values. The mode is the value that occurs most frequently, which, in this case, may not exist if no value is repeated.

Let's start by listing the provided times in ascending order: 65.4, 79.5, 83.2, 94.7, 99.3, 113.5, 115.2, 128.4.

The mean can be calculated by summing these values and dividing by their count:

Add all the times: 65.4 + 79.5 + 83.2 + 94.7 + 99.3 + 113.5 + 115.2 + 128.4 = 779.2

Divide by the number of students (8): 779.2 / 8 = 97.4

Therefore, the mean time is 97.4 minutes.

The median is the average of the fourth and fifth values since there's an even number of data points:

(94.7 + 99.3) / 2 = 97

Therefore, the median time is 97 minutes.

Since no value is repeated, there is no mode in this sample.

Answer 2

Answer: Mean = 97.4

Median = 97

Mode = 0

Step-by-step explanation:

Here, the given data,

65.4​, 79.5​, 83.2​, 113.5​, 128.4​, 99.3​, 94.7​, 115.2

Thus, total observation = 8

Since,
`\text{Mean} = \frac{\text{ Sum of all observation}}{\text{ Number of the observations}}`

`\text{Mean}=(65.2+79.5+83.2+113.5+128.4+99.3+94.7+115.2)/(8)`

`\text{Mean} =97.4`

The arrangement of data in increasing order,

65.4​, 79.5​, 83.2​, 94.7​, 99.3​, 113.5​, 115.2, 128.4​

Therefore,
`\text{Median} = \text{ A number that between 94.7 and 99.3}`

⇒
`\text{ Median} = (94.7+99.3)/(2)`

⇒
`\text{ Median} = 97`

Since, there is no repeated observation in the given data,

⇒ Given data has no mode.