Grade 7 Measures of Central Tendency Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) a Teacher Asked Her Students to Enter Their Blood Group in an Online Form. These Were the Entries

He has to organize this data so that he knows how many students of each blood group are present in his class.

Make a Frequency Distribution table for her to organize this data

Table Supporting: 1_A_teacher_asked_her_students_to_enter_their_blood_group_in_an_online_form_These_were_the_entries
Blood GroupTally markFrequency
A +
AB +
B +
O +

(a) What is the mode of this data?

(b) Those with blood group AB + are called universal recipients (people who can receive blood from anyone) . How many universal recipients does this class have?

(c) If the teacher՚s blood group is B + , what is the total number of people that have B + blood group in the class?

(2) Here is the Number of T-Shirt of Different Size Available in Shop

Table Supporting: 2_Here_is_the_number_of_Tshirt_of_different_size_available_in_shop
T-shirt sizeNumber of T-shirt Available
S17
M24
L28
XL15
XXL14
XXXL10

(a) Finding the difference in the highest and lowest T-shirt size is the same as finding the Mean, Mode or Range?

(b) Finding the average number of T-shirt per size is the same as finding the Mean, Mode or Range?

(c) Finding the shoe size that has the maximum number of pairs in stock is the same as finding the Mean, Mode or Range?

(3) Tick (√) True or False

(a) The mean of 3, 5, 6,8, 2, and 6 is 5

(b) The mean and median are different for 14, 17, 26,20, 21

(c) The median and range are same for 110,80, 50

(4) Find the Set of Three Number Whose Mean is 12 and Mode is 6

(5) Find the Set of Three Number Whose Mean is 50 and Mode is 15

(6) Solve

(a) The mean of twenty three number is 58. What is the sum of this twenty three number?

(b) Suppose that 4 is added to every number in the set. What will be the sum of the new twenty three number?

(c) What will be the mean of new twenty three number?

(7) a Random Umber between 11 to 20 is Chosen

(a) Write all possible outcomes

(b) Write down the number of favorable outcomes for each event and calculate the event՚s probability.

Which event has the highest probability of occurring?

Table Supporting: 7_A_random_umber_Between_11_to_20_is_chosen
EventNumber of favorable out comesP (event)
(i)An odd number is chosen
(ii)A multiple of 2 is chosen
(iii)Numbers less than11 is chosen
(iv)Multiple of 6 is chosen
(v)Number greater than 18 is chosen

(c) Write down a possible event (when a number from 11 to 20 is picked) keeping its probability in mind.

Table Supporting: 7_A_random_umber_Between_11_to_20_is_chosen
EventP (Event)
(i)
(ii)
(iii)

Answers and Explanations

Answer 1 (A)

  • Frequency distribution table of given data is as below,
Table Supporting: Answers_and_Explanations
Blood GroupTally markFrequency
A +///3
AB +///3
B +///////7
O +////4
  • Mode: That means Number (Data) appear more than any other number (data) .
  • From frequency distribution table it can be seen that student having blood group β€œB +” are more than any other.
  • Means blood group β€œB +” appear more than any other blood group.
  • That means β€œB +” is Mode of given data.

Answer 1 (B)

  • From frequency distribution table it can be seen that there are 4 number of student in the class who are universal recipients, means have β€œAB +” blood group.
  • Therefore, there are 4 universal recipients in the class.

Answer 1 (C)

  • From frequency distribution table it can be seen that there are 7 number of student having β€œB +” blood group.
  • If Teacher also have β€œB +” blood group therefore, now there are 8 number of people in class have β€œB +” blood group.

Answer 2 (A)

  • Highest T-shirt size in the shop is β€œXXXL”
  • And Lowest T-shirt size in the shop is β€œS”
  • The difference in the highest and lowest T-shirt size is β€œβ€
  • And this is same as the Range of T-shirt available in the shop.

Answer 2 (B)

  • To find the average number of T-shirt size available in the shop first so sum of number of T-shirt of all size, than divide this sum by total number of Size of T-shirt available in the shop.
  • Therefore,

  • Therefore, there are 18 number of average T-shirt per size available in the shop.
  • And this is same as the Mean of the data.

Answer 2 (C)

  • From data the T-shirt Size β€œL” has the maximum number in the stock.
  • And is same as the mode of the data given.

Answer 3 (A)

  • Mean: Average of given data.
  • Therefore;

  • Therefore mean of given number is β€œ5” .
  • Means Given statement is true.
  • The mean of 3, 5, 6,8, 2, and 6 is 5

Answer 3 (B)

  • Given number is; 14,17, 26,20 and 21.
  • Mean of given data

  • And for medial first arrange data (re-write data) in descending order.
  • That means: 14, 17,20, 21, and 26.
  • Now medial means; after writing the given number series/data in descending order, the number in the middle of the given number series/data is a Median.
  • Therefor Median of given data series is

  • Therefore Median and mode of given data is not same.
  • The mean and median are different for 14, 17, 26,20, 21

Answer 3 (C)

  • For medial first arrange data (re-write data) in descending order.
  • That means: 50,80, and 110
  • Now medial means; after writing the given number series/data in descending order, the number in the middle of the given number series/data is a Median.
  • Therefor Median of given data series is

  • Now Range: Range of given data means it՚s a difference between Highest (Maximum) and lowest (Minimum) number of given data.
  • From give data Maximum number is 110 and minimum number is 50.
  • Therefore range of given data:

  • Therefore Median and Range of given data is not same.
  • Therefore, The median and range are same for 110,80, 50

Answer (4)

  • Here given three number, so first we put three Blank as below.

  • As per given data mode of these three number is 6, so β€œ6” is appear more than any other number.
  • So can say,

  • Mean of the given number is β€œ12” , let guess the third number is

  • So, Set of three number is,

Answer (5)

  • Here given three number, so first we put three Blank as below.

  • As per given data mode of these three number is 15, so β€œ15” is appear more than any other number.
  • So can say,

  • Mean of the given number is β€œ50” , let guess the third number is

  • So, Set of three number is,

Answer 6 (A)

  • Given that mean of twenty three number is 58.
  • Mean means average of twenty three number is 58.

  • Therefore Sum of this twenty three number is 1334

Answer 6 (B)

  • Suppose 4 is added to every twenty three number in the set than for sum of new twenty three number,
  • Sum of old twenty three number is 1334.
  • Therefore;

  • Therefore sum of new twenty three number is 1426.

Answer 6 (C)

  • Therefore Mean of new twenty three number is 62.

Answer 7 (A)

  • All possible outcomes of random umber chosen from 11 to 20 is.

Answer 7 (B)

  • The favorable outcome of given event and its probability is as below,
Table Supporting: Answers_and_Explanations
EventNumber of favorable out comesP (event)
(i)An odd number is chosen5
(ii)A multiple of 2 is chosen5
(iii)Numbers less than12 is chosen1
(iv)Multiple of 6 is chosen2
(v)Number greater than 18 is chosen2
  • Therefore from above 2 event has highest probability of occurring

1. An odd number is chosen

2. A multiple of 2 is chosen

Answer 7 (C)

Table Supporting: Answers_and_Explanations
EventP (Event)
(i)
  • A multiple of 4 is chosen
  • A multiple of 3 is chosen
  • A number less than 14 is chosen
  • A number more than 17 is chosen
(ii)
  • A number multiple of 7 is chosen
  • A number multiple of 8 is chosen
  • A number multiple of 9 is chosen
  • A number multiple of 10 is chosen
  • A number less than 12 is chosen
  • A number greater than 19 is chosen
(iii)
  • A number greater than 11 is chosen
  • A number less than 20 is chosen

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