A meteorologist recorded the daily minimum temperatures, in degrees Celsius, at a high-alt… — GRE General Test

A meteorologist recorded the daily minimum temperatures, in degrees Celsius, at a high-altitude research station over a 7-day period: $3$ , $-5$ , $7$ , $-2$ , $10$ , $-8$ , and $2$ .

If $M$ represents the median of these daily minimum temperatures and $A$ represents the arithmetic mean, what is the value of $M - A$ ?

A
$-3$
B
$-1$
C
$0$
$1$ Cevap
E
$3$

Cevap

The value of

M - A

1

To evaluate

M - A

, first arrange the data set in ascending order:

-8, -5, -2, 2, 3, 7, 10

. Since there are 7 numbers, the median

M

is the middle (4th) value, which is

2

. Next, find the arithmetic mean

A

by taking the sum of the elements,

(-8) + (-5) + (-2) + 2 + 3 + 7 + 10 = 7

, and dividing by

7

, yielding

A = 1

. Finally, subtract the mean from the median:

M - A = 2 - 1 = 1

Adım Adım Çözüm

Sort the dataset in ascending order to find the median

M

The sorted list of 7 temperatures is:

-8, -5, -2, 2, 3, 7, 10

The median of a set with an odd number of elements is the middle value of the ordered dataset.

Identify the 4th element in the sorted dataset.

M = 2

In a dataset of 7 ordered values, the middle (4th) position represents the median.

Calculate the arithmetic mean

A

by summing all temperatures and dividing by 7.

Sum

= (-8) + (-5) + (-2) + 2 + 3 + 7 + 10 = 7

. Thus,

A = \frac{7}{7} = 1

The arithmetic mean is defined as the total sum of observations divided by the number of observations.

Compute

M - A

M - A = 2 - 1 = 1

Subtracting the mean from the median yields the required target value.

Anahtar Kavram

Calculating the median of a dataset requires arranging values in numerical order before identifying the central value.

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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Konular

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