Question

The table lists the number of items that 5 shops sold on a particular day. What is the mean absolute deviation of this data set?

A.
3.2
B.
4
C.
6.4
D.
9
E.
12.6

Answer 1

Answer: Option C. 6.4

Solution

1) Find the mean

Mean: M=(32+26+43+38+46)/5

M=(185)/5

M=37

2) Find the distance between each data value and the mean:

d1=Absolute value (Value 1 - Mean)

d1=Absolute value (32-37)

d1=Absolute value (-5)

d1=5

d2=Absolute value (Value 2 - Mean)

d2=Absolute value (26-37)

d2=Absolute value (-11)

d2=11

d3=Absolute value (Value 3 - Mean)

d3=Absolute value (43-37)

d3=Absolute value (6)

d3=6

d4=Absolute value (Value 4 - Mean)

d4=Absolute value (38-37)

d4=Absolute value (1)

d4=1

d5=Absolute value (Value 5 - Mean)

d5=Absolute value (46-37)

d5=Absolute value (9)

d5=9

3) Mean absolute deviation (MAD) is the average distance:

MAD=(d1+d2+d3+d4+d5)/5

MAD=(5+11+6+1+9)/5

MAD=(32)/5

MAD=6.4

Answer 2

Answer:

The correct answer option is C. 6.4

Step-by-step explanation:

First of all we need to find the mean of the given data set.

Mean = $\frac{32+26+43+38+46}{5}$

Mean = $\frac{185}{5}$

Mean $= 37$

To find the absolute mean deviation, we will use the following formula:

Mean Deviation = ∑ | x - μ | / N

To find  ∑ | x - μ |, we will find the difference of each value from the mean.

|32-37| = 5

|26-37| = 11

|43-37| = 6

|38-37| = 1

|46-37| = 9

∑ | x - μ | = 5 + 11 + 6 + 1 + 9 = 32

∑ | x - μ | / N = 32 / 5 = 6.4

Therefore, the absolute mean deviation for this data set is 6.4.