QQQ Stats 1 Chapter 2 v1, CHATPER 2 MEASURES OF LOCATION AND SPREAD. PDF

Preview

Summary

CHATPER 2 MEASURES OF LOCATION AND SPREAD. DRFROST...

Description

QQQ – StatsYr1 - Chapter 2 – Measures of Location & Spread (v1) Total Marks: 18 (18 = Platinum, 16 = Gold, 14 = Silver, 13 = Bronze)

1. The data below shows the ages 𝒙 of various people in the queue at a post office. 13 17 17 20 21 29 36 45 a. What is the mean age? b. What is the standard deviation of the age?

c. The data is coded using 𝑦 = deviation of 𝑦.

2.

𝑥−10 3

(1) (2)

. Determine the mean and standard (2)

The table shows the orbit durations, to the nearest year, of different comets. Time (years) 𝑡 Number of comets 𝑓

1-10 2

a. b. c. d. e. f.

11-20 5

21-25 7

26-40 4

You may use Σ𝑓𝑡 2 = 39923.75

41-60 12

Calculate the mean orbit time of a comet. (2) Use linear interpolation to estimate the median orbit time of a comet. (2) Show that the lower quartile is 20.9 years. (1) Find the interquartile range of the orbit times. (2) Find the standard deviation of the orbit time of a comet. (2) Ten more comets were added to the data, all with an orbit period of 20 years. Calculate the new mean. (2) g. There was a measurement error, and the orbit period of each comet should have been recorded as 5 years longer. Describe the effect on your answers to (a), (b), (c), (d) and (e). (2)

www.drfrostmaths.com

Solutions (Q2 © Edexcel)

Question 1 a. 24.75

A1 5750 8

b. 𝜎𝑥 = √ = 10.3

c. 𝑦 =

− 24.752

24.75−10

𝜎𝑦 =

3 10.3 3

M1 A1

= 4.92

B1ft

= 3.43

B1ft

Question 2 a. 𝑥 =

987.5 30

M1

= 32.9

b. 𝑄2 =

1 25.5 + ( 4

= 29.3 to 3sf

c. 𝑄1 = 20.5 +

A1 × 15)

0.5 ( 7 4.5

d. 𝑄3 = 40.5 + (

12

A1 × 5) = 20.9

× 20) = 48

𝐼𝑄𝑅 = 48 − 20.9 = 27.1

e. 𝜎 =

2 √39923.75 − (987.5 ) 30 30

= 15.8

f.

𝑥 =

987.5+10×20 30+10

= 29.7 g. (a) (b) (c) all increase by 5. (d) (e) unchanged.

www.drfrostmaths.com

M1 B1 B1 A1ft M1 A1 M1 A1 B1 B1...