Browse Cumulative frequency & box plots

31 questions at your level

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Cumulative frequency diagrams

11 questions

LessonNot started
The cumulative frequency diagram shows the battery life, in hours, of 120 mobile phones.24681020406080100120Battery life (hours)Cumulative frequency(a) Use the diagram to work out the frequency for each of the classes 0<t≤20 < t \le 2, 2<t≤42 < t \le 4, 4<t≤64 < t \le 6, 6<t≤86 < t \le 8 and 8<t≤108 < t \le 10.

(b) Work out an estimate for the mean battery life.
●●●●●Level 55 marksStart
150 people applied for a job. Each applicant sat a test marked out of 100. The cumulative frequency diagram shows their scores.2040608010020406080100120140Test scoreCumulative frequency(a) The 30 applicants with the highest scores will be invited to an interview. Use the diagram to estimate the lowest score an applicant needs in order to be invited to an interview.

(b) A newspaper claims that more than 40% of the applicants scored 45 or less. Use the diagram to decide whether this claim is correct. You must show your working.
●●●●●Level 56 marksStart

Quartiles & the interquartile range

14 questions

LessonNot started
During an experiment, 1111 temperatures were recorded in degrees Celsius. For these temperatures:
  • the median was 20 ∘20\,^{\circ}C
  • the lower quartile was 14 ∘14\,^{\circ}C
  • the upper quartile was 29 ∘29\,^{\circ}C
The temperatures are converted to degrees Fahrenheit using F=1.8C+32F = 1.8C + 32.

(a) Work out the median of the temperatures in degrees Fahrenheit.

(b) Work out the interquartile range of the temperatures in degrees Fahrenheit.
●●●●●Level 55 marksStart
A grower has two fields of sunflowers.

For the 120120 sunflowers in field P, the heights have
  • lower quartile 136136 cm
  • median 145145 cm
  • upper quartile 155155 cm
The heights, in centimetres, of a sample of 99 sunflowers from field Q are

128,134,140,148,152,157,166,172,195128, \quad 134, \quad 140, \quad 148, \quad 152, \quad 157, \quad 166, \quad 172, \quad 195

(a) Write down the median height of the sample from field Q.

(b) Work out the interquartile range of the heights of the sample from field Q.

(c) Estimate how many of the 120120 sunflowers in field P are taller than 155155 cm.

(d) Compare the heights of the sunflowers in field P with the heights of the sample from field Q.
●●●●●Level 57 marksStart

Box plots

12 questions

LessonNot started
The box plots give information about the distances, in km, travelled to work by the employees at two companies.

Company A, which has 200200 employees:102030405060Distance (km)Company B, which has 120120 employees:102030405060Distance (km)(a) Work out how many of the employees at Company A travel more than 3030 km to work.

(b) Jordan says, "The box for Company B is much wider than the box for Company A, so more employees at Company B travel a distance between their own company's lower quartile and upper quartile."

Is Jordan correct? You must show your working.
●●●●●Level 55 marksStart
Sam is drawing a box plot for a set of data. He knows that
  • the smallest value is 99,
  • the range is 4646,
  • the median is 3434,
  • the interquartile range is 1818,
  • the median is 77 more than the lower quartile.
(a) Work out the largest value.

(b) Work out the lower quartile.

(c) Work out the upper quartile.

(d) Sam says that the same number of values lie between the lower quartile and the median as lie between the upper quartile and the largest value.

Is Sam correct? Give a reason for your answer.
●●●●●Level 56 marksStart