A set of data that shows temperature highs for 10 days and satisfies all conditions below mean:72 median:74 mode:68 range:21

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A set of data that shows temperature highs for 10 days and satisfies all conditions below mean:72 median:74 mode:68 range:21

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Mathematics Thanh Hà 1 week 2021-07-22T11:40:18+00:00 2021-07-22T11:40:18+00:00 1 Answers 4 views 0

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Nem · Answer 1 · 2021-07-22T11:41:57+00:00

Answer:

$58, 68, 68, 68, 74, 74, 76, 77, 78, 79$

Step-by-step explanation:

Given

$n=10$

$Mean = 72$

$Median = 74$

$Mode = 68$

$Range = 21$

Required

The complete dataset

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From the mean, we have:

$Mean = \frac{\sum x}{n}$

This gives:

$72 = \frac{\sum x}{10}$

Cross multiply

$\sum x = 72 * 10$

$\sum x = 720$

This means that the sum of all elements of the dataset is 720

Next, we test the median

Since n = 10, then:

$Median = \frac{n + 1}{2}$

$Median = \frac{10 + 1}{2}$

$Median = \frac{11}{2}$

$Median = 5.5th$

This implies that the median is the average of the 5th and 6th item.

So, we have:

$Median = \frac{5th + 6th}{2}$

Cross multiply

$5th + 6th = 2 * Median$

$5th + 6th = 2 * 74$

$5th + 6th = 148$

This means that the 5th and 6th element add up to 148

Also, we have:

$Mode = 68$

This means that 68 has to appear at least twice in the dataset

$Range = 21$

This implies that the difference between the highest and the least is 21.

The dataset that satisfies the above condition is:

$58, 68, 68, 68, 74, 74, 76, 77, 78, 79$

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A set of data that shows temperature highs for 10 days and satisfies all conditions below mean:72 median:74 mode:68 range:21