6. Raw Data: 3,5,7,4,3, 8, 6, 6,9, 6,7,8,9,3, 3, 9 There are 16 data items Find: a) Mean b) Median c) Midrange d) Mode 7. Find t

Question

Paul [167]

3 years ago

5

6. Raw Data: 3,5,7,4,3, 8, 6, 6,9, 6,7,8,9,3, 3, 9 There are 16 data items Find: a) Mean b) Median c) Midrange d) Mode 7. Find t

he standard deviation of the data in question 6

Mathematics

1 answer:

Hoochie [10] · Answer 1 · 2022-03-25T20:57:50+03:00

Answer:

6.a. Mean= 6

b. Median=6

c Midrange=6

d.Mode=4

7.Standard deviation=2.2079

Step-by-step explanation:

Given data

3,3,3,3,4,5,6,6,6,7,7,8,8,9,9,9

Total data items,n=16

Sum o data items=96

a. Mean= $\frac{sum\;of\;data\;items}{total\;data\;items}$

Mean= $\frac{96}{16}$

Mean=6

b.If total number of items are even then

Median= $\frac{\frac{n}{2}^{th}\;observation+\left(\frac{n}{2}+1\right)^{th}}{2}$

Median= $\frac{\frac{16}{2}^{th} observation+\left(\frac{16}{2}+1\right)^{th} observation}{2}$

Median= $\frac{8^{th} observation+9^{th} observation}{2}$

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

Median= $\frac{12}{2}$

Median=6

c. Midrange= $\frac{lower\;value+highest\;value}{2}$

Lower data item=3

Highest data item=9

Midrange= $\frac{3+9}{2}$

Midrange= 6

d.Mode : It is defines as a number that appear most often in a set of numbers.

Mode=3

7. Mean $\bar x=6$

$\mid x-\bar x\mid$ ${\mid x-\bar x\mid}^2$

3 9

2 4

1 1

0 0

1 1

2 4

3 9

$\sum{\mid x-\bar x\mid}^2=78$

n=16

Standard deviation= $\sqrt{\frac{\sum{\mid x-\bar x}^2}{n}}$

Standard devaition= $\sqrt{\frac{78}{16}}$

Standard deviation= $\sqrt{4.875}$

Standard deviation of data =2.2079