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1 PLC Papers Created For: Year 11 Topic Practice Paper: Histograms
2 Histograms with unequal class widths 1 Grade 6 Objective: Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous data) Question 1 The table shows the weight of 815 parcels handled by a sorting office in one day. a) Draw a fully labelled histogram to show the weights of the parcels. (4) b) Estimate the number of parcels that weighed more than 2500 grams..
3 Question 2 The histogram and the frequency table show some information about how much time vehicles spent in a car park. Time, minutes Frequency 0 < x < x < x < x Total Frequency Density Time, minutes a) Use the information to complete the histogram b) Use the histogram to find the missing frequencies in the table Total for question 4 marks Total /10
4 Histograms with unequal class widths 2 Grade 6 Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table shows the length of 678 phone calls made at a call centre Time, secs Frequency 0 < x < x < x < x Total 678 a) Draw a fully labelled histogram to show the length of the phone calls. (4)
5 b) Estimate the number of phone calls that lasted more than 2 minutes. Total for question 6 marks
6 Question 2 The histogram and the frequency table show some information about the height of some students Height, cms Frequency 130 < x < x < x < x < x Total 400
7 Frequency Density Height, cms a) Use the information to complete the histogram b) Use the histogram to complete the table Total for question 4 marks Total /10
8 Histograms with unequal class widths 3 Grade 6 Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table and histogram show the weights of some snakes. Weight, grams Frequency 250 < x < x < x < x < x Total
9 a) Use the information to complete the histogram b) Use the histogram to find the missing frequencies in the table c) Calculate an estimate for the median d) This particular breed of snakes need to reach 420 grams before they are able to reproduce. What percentage of these snakes are able to reproduce. (4) Total for question 10 marks Total /10
10 Histograms with unequal class widths 4 Grade 6 Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table and histogram show the lengths of some pythons. Length, cms Frequency 30 < x < x < x < x < x Total Length, cms
11 a) Use the information to complete the histogram b) Use the histogram to find the missing frequency s in the table c) Calculate an estimate for the mean d) Estimate the median python length. (3) (3) Total for question 10 marks Total /10
12 PLC Papers Created For: Year 11 Topic Practice Paper: Histograms
13 Histograms with unequal class widths 1 Grade 6 SOLUTIONS Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table shows the weight of 815 parcels handled by a sorting office in one day. a) Draw a fully labelled histogram to show the weights of the parcels Frequency Density Weight w, grams (4)
14
15 b) Estimate the number of parcels that weighed more than 2500 grams 0.12 x 1500 = (180) M1 180 A1.. Question 2 The histogram and the frequency table show some information about how much time vehicles spent in a car park. Time, minutes Frequency Class Width Freq. Density 0 < x < x < x < x Total Frequency Density Time, mins a) Use the information to complete the histogram
16 b) Use the histogram to find the missing frequencies in the table 1.5 x 10 = 15 B1 1.8 x 20 = 36 B1 15 and 36 Total for question 4 marks Total /10
17 Histograms with unequal class widths 2 Grade 6 SOLUTIONS Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table shows the length of 678 phone calls made at a call centre Time, secs Frequency Class Width Freq. Density 0 < x < x < x < x Total 678 a) Draw a fully labelled histogram to show the length of the phone calls Frequency Density Time, secs (4)
18 b) Estimate the number of phone calls that lasted more than 2 minutes. 4 minutes = 4 x 60 secs = 240 secs = 60 mins 60 x 1.5 = (90 calls) M1 90 calls A1 Total for question 6 marks
19 Question 2 The histogram and the frequency table show some information about the height of some students Height, cms Frequency Class Width Freq. Density 130 < x < x < x < x < x Total Frequency Density Height, cms a) Use the information to complete the histogram b) Use the histogram to complete the table Total for question 4 marks Total /10
20 Histograms with unequal class widths 3 Grade 6 SOLUTIONS Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table and histogram show the weights of some snakes. Weight, grams Frequency Class Width Freq. Density 250 < x < x < x < x < x Total FREQUENCY DENSITY Weight, grams
21 a) Use the information to complete the histogram Middle bar frequency = 40 class width = 25 frequncy density = 40/25 = 1.6 M1 Draw in scale M1 Draw rest of bars correctly A1 b) Use the histogram to find the missing frequencies in the table (3) Correct frequencies A2 c) Calculate an estimate for the median 200 snakes, median at 201/2 = th (condone 100 th ) 200 ( (25)) 25 / 1.6 = M = ( ) 334 grams A1 d) This particular breed of snakes need to reach 420 grams before they are able to reproduce. What percentage of these snakes are able to reproduce = x 0.4 = 12 snakes M = / 200 x 100 =(26%) M1 26% A1 (3) Total for question 10 marks Total /10
22 Histograms with unequal class widths 4 Grade 6 SOLUTIONS Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table and histogram show the lengths of some pythons. Length, cms Frequency Class Width Freq. Density 30 < x < x < x < x < x Total 180
23 FREQUENCY DENSITY Length, cms a) Use the information to complete the histogram 50 / 20 = 2.5 (f.d.) Label the frequency density axis Complete histogram bars M1 A1 b) Use the histogram to find the missing frequency s in the table 50 x 0.7 = (35) M1 for at least one calculation 30 x 2.2 = (66) A1 for both correct
24 c) Calculate an estimate for the mean 35 x x x x x 35 = = M / 181 = 78.1cm M1 d) Estimate the median python length. 78.1cm A1 (3) ( )/2 = 91 First three bars = 80, need 11 more for median. M1 11 / 2.2 = 5 M = 75 cms 75cms A1 (3) Total for question 10 marks Total /10
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