Question

Find the mean for the following frequency tables. (Round your answers to one decimal place.)

(a)	Grade Frequency 49.5–59.5 2 59.5–69.5 3 69.5–79.5 6 79.5–89.5 14 89.5–99.5 5

(b)	Daily Low Temperature Frequency 49.5–59.5 50 59.5–69.5 30 69.5–79.5 15 79.5–89.5 1 89.5–99.5 0

(c)	Points per Game Frequency 49.5–59.5 14 59.5–69.5 32 69.5–79.5 15 79.5–89.5 21 89.5–99.5 2

Answer 1

Solution:-

Solution:

a)

Class (1)	Frequency (f) (2)	Mid value (x) (3)	d=x-A/h=x-74.5/10 A=74.5,h=10 (4)	f⋅d (5)=(2)×(4)
49.5 - 59.5	2	54.5	-2	-4
59.5 - 69.5	3	64.5	-1	-3
69.5 - 79.5	6	74.5=A	0	0
79.5 - 89.5	14	84.5	1	14
89.5 - 99.5	5	94.5	2	10
---	---	---	---	---
	n=30	-----	-----	∑f⋅d=17

Mean =A+∑fd/n⋅h

=74.5+17/30⋅10

=74.5+0.5667⋅10

=74.5+5.6667

=80.2

b)

Class (1)	Frequency (f) (2)	Mid value (x) (3)	d=x-A/h=x-74.5/10 A=74.5,h=10 (4)	f⋅d (5)=(2)×(4)
49.5 - 59.5	50	54.5	-2	-100
59.5 - 69.5	30	64.5	-1	-30
69.5 - 79.5	15	74.5=A	0	0
79.5 - 89.5	1	84.5	1	1
89.5 - 99.5	0	94.5	2	0
---	---	---	---	---
	n=96	-----	-----	∑f⋅d=-129

Mean =A+∑fd/n⋅h

=74.5+-129/96⋅10

=74.5+-1.3438⋅10

=74.5+-13.4375

=61.1

c)

Class (1)	Frequency (f) (2)	Mid value (x) (3)	d=x-A/h=x-74.5/10 A=74.5,h=10 (4)	f⋅d (5)=(2)×(4)
49.5 - 59.5	14	54.5	-2	-28
59.5 - 69.5	32	64.5	-1	-32
69.5 - 79.5	15	74.5=A	0	0
79.5 - 89.5	21	84.5	1	21
89.5 - 99.5	2	94.5	2	4
---	---	---	---	---
	n=84	-----	-----	∑f⋅d=-35

Mean =A+∑fd/n⋅h

=74.5+-35/84⋅10

=74.5+-0.4167⋅10

=74.5+-4.1667

=70.3