Express the difference in the means as a multiple of their ranges.

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12-03-2018
Mathematics

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Express the difference in the means as a multiple of their ranges.

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virtuematane virtuematane · Answer 1 · 2019-05-29T11:24:21+02:00

Answer:

Hence, the difference in mean is represented as:

12=2.5×5

where 5 is the range and 12 is the difference in the mean.

Step-by-step explanation:

Shade plant Height (in.)

7 11 11 12 9 12 8 10

Minimum value=7

and Maximum value=12

Range=Maximum value-Minimum value

This means that Range is: 12-7=5

Also, the mean is calculated as follows:

[tex]Mean=\dfrac{7+11+11+12+9+12+8+10}{8}\\\\\\Mean=\dfrac{80}{8}\\\\\\Mean=10[/tex]

Sun Plant heights (in.)

21 24 19 19 22 23 24 24

Minimum value=19

and Maximum value=24

Range=Maximum value-Minimum value

This means that Range is: 24-19=5

Also, the mean is calculated as follows:

[tex]Mean=\dfrac{21+24+19+19+22+23+24+24}{8}\\\\\\Mean=\dfrac{176}{8}\\\\\\Mean=22[/tex]

Difference in mean is: 22-10=12

Also, the range of both the set is: 5

Hence, the difference in mean could be expressed as:

12=5×n

Hence, n=2.5

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-05-04T18:13:35+02:00

The expression (12 = 5×2.4) represents the difference in the means as a multiple of their ranges if the mean for the first data set is 10 and for the second data set is 22.

What is mean?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

For the first data:

The mean can be calculated as follows:

[tex]\rm Mean = \frac{\sum x}{n}[/tex]

[tex]\rm Mean = \frac{7 + 11+ 11+ 12 + 9+ 12+ 8+ 10}{8}[/tex]

Mean(1st data set) = 10

For range:

The minimum value in the data set = 7

The maximum value in the data set = 12

Range = 12 - 7 ⇒ 5

For the second data set:

The mean can be calculated as follows:

[tex]\rm Mean = \frac{\sum x}{n}[/tex]

[tex]\rm Mean = \frac{21 + 24 + 19 + 19 + 22 + 23 + 24 + 24}{8}[/tex]

Mean(2nd data set) = 22

For range:

The minimum value in the data set = 19

The maximum value in the data set = 24

Range = 24- 19 ⇒ 5

Difference in means = 22 - 10 ⇒ 12

Since the range is the same for both the data set.

From the problem:

12 = 5×n

n = 2.4

Thus, the expression (12 = 5×2.4) represents the difference in the means as a multiple of their ranges if the mean for the first data set is 10 and for the second data set is 22.

Learn more about the mean here:

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