Mathematics and statistics, Exercises of Mathematics

Mathematics and statistics, Questions and answers

Typology: Exercises

2021/2022

Uploaded on 12/02/2025

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FREQUELCY TREES - PRASTICE QUESTTO!{S
1.
There are 150 pupils in Year 1O.
Pupils either have school lunches or packed lunches"
79 of the pupils are boys.
45 girls have school lunches and 39 boys have school iunches.
Complete the frequency tree.
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r-: - ---^ I 1, ,--..-1. .-. -:
-fichn*l l.r-rnches
Faclted. hilrc&:es
2.
There are 95 cars in a car park.
25 af the cars are white.
13 of ttre non-white cars are convertibles and 2l of the white cafs are not convertibles.
{a} Complete the freql.rency tree.
'Lff:r."ec"tifoIes
}l*t c*r:s'*stibles
Cc*r-'ert{bl,es
".: - - .-. -. -- - ".- -". t-.1 - ,-
t!,,_ _.._.'_i . :- t-_)-.1=.]
(b) A car is picked at random. What is the probabiiity that the car picked is a white
convertible? I
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FREQUELCY TREES - PRASTICE^ QUESTTO!{S

There are 150 pupils in^ Year^ 1O. Pupils either have school^ lunches^ or^ packed lunches"

79 of the pupils are boys.

45 girls have school lunches and^ 39 boys have school^ iunches.

Complete the frequency^ tree.

rnetotutor

Srhq:sl1u:chs

r-: (^) - ---^ I 1, ,--..-1. .-. -:

-fichn*l l.r-rnches

Faclted. hilrc&:es

There are 95 cars in a^ car^ park.

25 af the cars are white. 13 of ttre non-white cars are^ convertibles^ and^ 2l^ of^ the^ white^ cafs^ are^ not^ convertibles.

{a} Complete^ the^ freql.rency^ tree.

'Lff:r."ec"tifoIes

}lt cr:s'*stibles

Cc*r-'ert{bl,es

".: t!,,_ (^) - (^) - .-....'i (^) -. -- - (^). :-".- -".t-)-.1=.] t-.1 (^) - ,-

(b) A car is picked^ at^ random. What^ is^ the^ probabiiity^ that^ the^ car picked^ is^ a^ white

convertible? (^) I ,+ q

86 people took driving tests last rnonth. 30 of the people lvere male^ " 90% of tl:e rnales passed^ their^ test,^ and^ 75ala^ of^ the^ females passed^ their^ test.

(a) Complete the kequency tree.

Fassed test

Failed test

Passed test

Faileci test

40'/,

7 s'/,

olr

sI (^) 5r*= (^) +z

30= (^) La

{b} How^ many^ of^ the 86^ people t++Z (^) c

A ca-fe setr1s baguettes and rolls in two types - ham and^ cheese.

Last week, they sold 26 ham haguettes and 45^ cheese^ rolls. 75 of the totaL l2O iterns^ sold were^ rolls.

Complete the frequency tree.

failed their test?

l- ar*,

t.

Archie wanted to know whether he shor-rld travel to work^ by bus or trairi.

He made note of the number of times he was late to work on 85 days last year. Archie travelled by bus on 35 days.

He was late travelling by bus on 7 days and on tirne travelling by train on 41 days.

{a} Cornpiete^ the^ freqr"rency^ tree^ below.

{b} Con'rpare^ the^ percentage^ ol^ days^ Archie^ was^ late^ travell.ing^ by^ bus^ with^ the^ percentage

of days Archie was late travelling by train.

tsus * 1/?g=^ ZO'/, Tra,n* S/so =

l8'1,

25O students can-r play rugby or football, and cricket cr tennis. 150 play football. 35 play^ tennis ancl rugby. 5O% of the (^) students who play football play cricket.

Cornplete the frequency tree bel.ow.

ftq (^) Fgrgg,nlr45e o[^ earyr^ &rchie uot$ (^) ta.te b, b-s kr41 (^) tr1f LL^rrn (^) by (^) LA3A-,

6{r/, 6I IGC>^ 4

{}n tin:e

{_}r1 (^) L1fl1e

A hospital employs doctors and nurses, on^ full-time^ and^ part-time^ contracts.

The hospital employs^ 60O^ staff^ in^ total.

75oh af^ the^ staff at the^ hospital^ are nurses" The hospital ernploys 95 part-tirne^ nurses.

The hospital ernploys^ 7O^ more^ full-time^ doctors^ than part-tirne^ doctors.

{a} Complete^ the^ f,requency^ tree below. Fu11-time

I)octors Part-time

Fri11-time

-75'/. (^) oF 6cO:- t+5o

(b) Hcw rnany part-tirne^ staff^ do^ the^ hospita-l^ emptroy? tto (^) *45 a (^) t

A group^ of people^ are standing on^ a^ train^ platform-

They are wearing either shorts or^ trousers,^ and^ either^ shoes^ or^ sandals" There are 23 people^ wearing shorts.

There xe 4O^ people^ wearing^ shoes.

4 of the 42 peapLe wearing trousers^ are^ wearing^ sandals.

How rnany people^ are^ wearing^ saldals?

Fart-tir,l:re