Statistical Measures and Calculations

An ordinary fair dice is rolled. Circle the probability of rolling a 4.

Miss Wardle records information about homework completion for her class. How many males did **not** complete this piece of homework?

What is the probability that a student, chosen at random, completed this piece of homework?

The number of lambs born on each of the first 10 days in April are given. 8, 11, 9, 14, 12, 14, 10, 15, 14, 13 Circle the first 4-point moving average.

The formula used to calculate a birth rate is: Birth rate = (number of live births recorded / total population) × 1000 The population of Germany in 2017 was approximately 80 000 000. Use the table on page 11 and this information to estimate the approximate number of live births recorded in Germany in 2017.

Natalie is selling her house. At an asking price of £135 000, she is advised that the house would definitely sell within one month. For each additional £1000 on the asking price, the risk of **not** selling within any one month increases by 0.05. Natalie wants £150 000 for her house. At £150 000, what is the risk that she will **not** sell her house within one month?

At £150 000, what is the risk that she will **not** sell her house within two months?

Using the information given, what is the minimum price for which the house will apparently **never** sell?

The graph shows changes in private and public sector pay and the Consumer Price Index (CPI). What does CPI measure?

An index for public sector pay was 100 in Jan 2010. By May 2012, it had risen to 104.5. By what percentage, approximately, did public sector pay increase between Jan 2010 and May 2012? choose your answer.

Jim says, “The index number for CPI is 120 to the nearest whole number for May 2018 with Jan 2010 as base. So the index number for CPI for Jan 2010 with May 2018 as base will be 80 to the nearest whole number.” Evaluate **all** of Jim’s statement. Use calculations, where necessary, to show if he is correct.

A set of data is ordered from smallest to largest. What is the name given to the measure that is one quarter along the ordered data?

Look at these sets of data. Which data set has a different range to the others? A: 2, 4, 5, 5, 7, 8 B: 0, 5, 3, 6, 1, 4 C: 9, 8, 7, 7, 6, 5 D: 5, -1, 3, 2, 0, 1

The probability that a biased coin lands on heads is 2/5. What is the probability that this coin lands on tails?

The mean mass of these 9 Vizslas is 23 kg. Calculate their mean height.

One student is chosen at random. What is the probability that they go to the museum?

Sanders owns a chicken farm where the chickens can roam freely. He is investigating where the chickens tend to go in their field. He divides the field up into 9 squares and counts the number of chickens in each square. Here are the raw data showing how many chickens are in each square. There is a food tray in the bottom right square. What is the probability that a chicken, chosen at random, is in the square with the food tray?

54 000 people are represented in the pie chart. The angle for the Labour sector is 120°. Work out how many of them voted for Labour.

The table shows information about the heights of a sample of 100 trees in a forest. Complete the table below to show the cumulative frequencies for the data.

It is still possible to correctly work out the median number of cupcakes from the stem and leaf diagram. Work out this median.

Mumps rate = (Number of confirmed cases / Total population) × 1000. The population of England in 2011 was estimated by the census to be 53,012,456. Show that the mumps rate for England in 2011 was 0.043 to 3 decimal places.

Here is an experiment which is designed to find the best trained dog out of Troy, Buddy, Bruno, Murphy and Bumble. Each of the five owners asks their dog to sit and then walks away. The time for which each dog sits is recorded. The experiment is repeated 4 more times. Here are the data for the five dogs. The dog which sits for the longest average time is declared the winner. Give a reason why each of the three dogs stated below could be declared the winner. In each answer you must state or calculate appropriate measures. - Buddy - Bruno - Murphy

This table also shows information about reduced journey times from London. Work out the missing time and percentage in the Preston row.

Two fair spinners, each numbered 1 to 8, are spun. The numbers they land on are added up. What is the probability the total is 16?

Which of these data lists is bi-modal **and** has the mean double the median?

The picture gives the risk of getting lung cancer. Based on the picture, how many out of every 1000 women who have **never smoked** are expected to get lung cancer?

How many times greater is the risk of getting lung cancer for a man who is a **heavy smoker** compared with a man who has **never smoked**?

A tech company's website offers rewards according to how many days you visit it. The table shows the number of rewards achieved by a sample of 500 customers. Show, with working that, for this sample, median = interquartile range.

Use calculations to confirm that there are no outliers in the **new** sample of 500 customers. You must show your working.

Once the race is run, Angelina notes the order in which the competitors finished, from 1st to 15th position. She also ranks the resting heart rate data from lowest to highest. She calculates that the value of Σd² = 60, where d is the difference in the ranks. Show that the value of Spearman's Rank Correlation Coefficient (SRCC) is 0.89 (to 2 decimal places). Use SRCC = 1 - (6Σd²) / (n(n² - 1))

Calculate an estimate of the number of squirrels in the forest.

Maisy has her house valued each year. The table shows the percentage increase in its value, written as a multiplier, over each of the last 5 years. Maisy wants to know the average percentage increase over the 5 years. She works out the arithmetic mean of the percentage increases (6.7%, 1.3%, 0.8%, 0.5%, 12.6%) and gets 4.4%. Maisy has used the wrong method. Name the measure she should have calculated.

A fair coin is tossed four times. Circle the probability of getting 'tails' on all 4 tosses.

Which one of these is **not** a measure of spread?

This table also shows information about reduced journey times from London. Work out the missing time and percentage in the Preston row.

There are variations in the number of sunspots seen per month throughout the year. How could you smooth out these variations?

There are 7 players who can play for a snooker team: Micky, Katie, Niles, Tommo, Paul, Jonno and Emma. Each week four players are needed to make up the team. One week, Micky and Katie are chosen for the team and the other two players are chosen at random. What is the probability that Niles is also in the team?